What criteria were used in collecting the Scriptures (Canon) which we know today as the Holy Bible. I'm not looking for new theological hypotheses here, just established ones. For example, how did they decide that a Scripture (say Mark) was canonical?

John I'm keen to keep this question in it's wider form, are you willing to allow that? You may yet get an even more in-depth survey that includes more information specifically helpful to you but it seems unfair to narrow the scope after Noah has answered?
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Jack DouglasSep 16 '13 at 18:07

On an anecdotal note, have you ever read the Gospel of Thomas? When one reads the other Scriptures (for example, those discovered in the city of Nag Hammadi) the comparisons are more objective than subjective. That is, the assumptions, content, and tone appear in stark contrast to what stand as the 27 books of the New Testament. In other words, the most casual comparison will yield the most stark of contrasts (in most cases).
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JosephJun 21 '14 at 14:29

2 Answers
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The cannon of the Torah and of the Prophets were settled by 4th century BCE (earlier for the Torah), and we don't have much evidence as to what criteria were used. We don't know which books were most controversial, and we don't know which books were excluded.

The cannon of the Writings was settled around the 1st or 2nd century CE. Since this was after Christianity and Judaism split, they ended up making different choices of which books to include or exclude. On the Jewish side, one major criteria was only using texts which were known to have Hebrew originals, while on the Christian side the main language used was Greek and so Jewish texts written in Greek were also included. The books considered scripture by Christians but not by Jews are what are now called the Apocrypha. We know some books which were widely read at the time which were not canonized by either group (for example, Jubilees) which is only canon in the Ethiopian church), but we don't really know why.

The New Testament cannon formed gradually over the first few centuries CE, and was largely settled sometime in the 5th century. (For example, all our extant 4th century bibles contain books which are not now considered cannon.) Several books which made the modern canon were very controversial at the time: 2-3 John, 2 Peter, Jude, and Revelation (called the Antilegomena). Several very popular books came close to acceptance but were eventually rejected (The Apocalypse of Peter, 1 Clement, the Shepherd of Hermas), these are sometimes called New Testament apocrypha. It is important to realize that not all groups came to the same conclusions. In particular, the Syriac-speaking Oriental Orthodox churches did not accept the Antilegomena for centuries (indeed some branches still don't). The Armenian, Georgian, and Ethiopian churches also have slightly different cannons of the New Testament.

For the New Testament we do have records of some of the arguments over what was to be included, and the main criteria seem to be:

The book should be "orthodox," that is it should agree with the mainstream teachings of the church.

The book should be widely read and popular, and not only preferred by specific subgroups.

The book should be written by an apostle. (Or more accurately, should be thought to have been written by an apostle by the people making the decision.)

At various later times, the canon has been reconsidered or modified. In particular, during the Reformation many Protestant groups chose to remove the Apocrypha and use the Jewish canon of the Tenakh instead (in part because they wanted to use the original Hebrew texts rather than the Latin translations). Also some protestants reconsidered the canonical status of certain books of the New Testament, for example Luther questioned James. The Lutheran New Testament places at the end the books that Luther questioned, though I think they still consider them canon.

The Old Testament is the same as the Jewish Scripture, although not necessarily in the same order, and with some verses split up differently. It can be considered heritage for the most part, although Athanasius did not consider Esther to be Scriptural. The Apocrypha were never considered Scripture by the Jews. Again, Athanasius did not consider these Scripture, but said they were "appointed by the Fathers to be read by those who newly join us, and who wish for instruction in the word of godliness." Some early church leaders quoted them as strongly as Scripture, and over time they became accepted as much as Scripture. This was an issue during the Reformation, because Protestants rejected the Apocrypha. At the Council of Trent, the Catholic church responded by including the Apocrypha in Scripture as Deuterocanonical.

The New Testament begin with the writing of the apostles. In some cases (you mentioned Mark) the writer was associated with an apostle, and wrote what the apostle said. Mark is linked with Peter, and Luke is linked with Paul. An important criteria that has been used involves consistency. The Gospel of Thomas and the Gospel of Judas were rejected early, because it was unclear exactly when and where they was written, and because each disagreed with the writings of the other apostles (minority reports). The conclusion was made that they weren't really written by them. This is where we get the term Catholic (universal) church. Its authority was a quorum of all the apostles and their testimony. Also, considering that Paul write most of the New Testament, recall that Peter validated Paul's writing (2 Peter 3:16).

James was written by James the elder of Jerusalem (Jesus' brother) and Jude was closely associated with him. Martin Luther was somewhat against including James as Canonical due to the lack of grace in the tone of the epistle. He kept it, calling it an epistle of straw.

Nobody knows who wrote Hebrews or how it became canonical. It has had an assumed Pauline authorship, but always with people challenging it.

One thing to consider about all of Scripture (and this is a big part of being accepted or rejected), that the Scriptures we have agree extremely well on doctrine. There are some hard passages, but overall the Scripture is very consistent. Some of the rejected Apocryphal books were inconsistent with other -- accepted -- books. The gospels of Thomas and Judas were inconsistent with the teachings in the other Gospels. Finally, for the most part, the Canon of Scripture was very well agreed upon by the early church fathers. At least some of this agreement is thought to be due to the access they had to the apostles' testimony. Many had first- or second-hand access to Jesus or the apostles.